How to Correctly Integrate S(x(x+1)^(1/2)) dx?

[tjohn101]

Homework Statement

S(x(x+1)^1/2) dx

Homework Equations

The Attempt at a Solution

u=x+1
du=1
x=u-1

S(x(u)^1/2) du

S(((u-1)(u)^1/2) du

S((u²-u)^1/2) du

S(u-u^1/2) du

S((1/2)u²-(2/3)u^3/2)

=(1/2)(x+1)²-(2/3)(x+1)^3/2) + COnline homework says it's wrong... Where did I mess up?

 

[tiny-tim]

Hi tjohn101!

(have an integral: ∫ )

S(((u-1)(u)^1/2) du

S((u²-u)^1/2) du

S(u-u^1/2) du

Neither of these lines is correct.

(u-1)√u = u√u - √u

 

[tjohn101]

Ahhhh thank you. I didn't notice I had done that :/

 

[tjohn101]

Hmmm I ended up getting

(2/5)(x+1)^5/2-(2/3)(x+1)^3/2 + C

Sound right?

 

[tiny-tim]

Hi tjohn101!

(just got up :zzz: …)

Yes … but perhaps you should put it in the same form as the question, ie √(x+1) times an ordinary polynomial in x ?

 

[tjohn101]

Thank you for your help!